1. Field of the Invention
The present invention relates to signal processing receivers, and, more specifically, to equalizing signals received by such devices.
2. Description of the Related Art
Overview of Prior-Art Receiver
FIG. 1 shows a block diagram of one implementation of a prior-art receiver 100 that uses a pilot channel to equalize (e.g., initialize (“train”) and track) a received signal. Receiver 100 has upstream processing 102, chip-rate normalized-least-mean-squares (NLMS) equalizer 104, de-scrambler and de-spreader 106, and downstream processing 108. Upstream processing 102 performs pre-equalization processing which might include analog-to-digital conversion, root raised-cosine filtering, or other processing to prepare a received signal for equalization. NLMS equalizer 104 receives digital data y(i) from upstream processing 102, equalizes signal y(i) to closely approximate the original pre-transmission signal, and outputs equalized signal {circumflex over (x)}(i) to de-scrambler and de-spreader 106. De-scrambler and de-spreader 106 removes the scrambling code and spreading sequences from equalized signal {circumflex over (x)}(i) and outputs soft symbols r(n). Soft symbols r(n) are then processed by downstream processing 108, which might include symbol estimation, data symbol de-mapping, or other post-equalization processing for recovering one or more output data streams from the received signal.
NLMS equalizer 104 equalizes digital signal y(i) using an update loop which comprises finite impulse response (FIR) filter 110, coefficient updater 112, and error calculator 114. FIR filter 110 receives incoming digital signal y(i), applies coefficients w(i) to signal y(i), and outputs equalized signal {circumflex over (x)}(i). Coefficients w(i) are calculated by coefficient updater 112 using (1) incoming signal y(i) and (2) an error signal e(i) received from error calculator 114. Error signal e(i) and coefficients w(i) are continuously updated at a maximum rate of one update per chip interval.
Coefficient Calculation Using a Normalized-Least-Mean-Squares Approach
Coefficients w(i) may be calculated using any one of a number of approaches commonly known in the art. According to the embodiment of FIG. 1, coefficient updater 112 receives signal y(i) and error signal e(i) and calculates new coefficients w(i+1) using a normalized-least-mean-squares (NLMS) approach. The NLMS approach is a variation of the least-mean-squares (LMS) approach, wherein each new coefficient w(i+1) is calculated as shown in Equation (1) below:wLMS(i+1)=wLMS(i)−μ∇wE[|e(i)2|],  (1)where ∇w is the gradient of the expected value E[|e(i)|2] of error signal e(i), and μ is the update step size.
The expected value E[|e(i)|2] (a.k.a., mean squared error (MSE)) can be represented as an “error performance surface.” A gradient descent approach is used to step across the surface to arrive at the minimum-mean-squared error (MMSE), which is represented by a local minimum on the surface. As the MSE of Equation (1) approaches the MMSE, the accuracy of tap weights w(i) increases. Substituting an instantaneous estimate for the expectation of Equation (1) yields the particular LMS calculation of Equation (2) as follows:wLMS(i+1)=wLMS(i)−Δy(i)e*(i),  (2)where a small scalar is chosen as the step size Δ and e*(i) is the complex conjugate of error signal e(i). To obtain the NLMS coefficient wNLMS(i+1), LMS Equation (2) is normalized to produce Equation (3) as follows:
                                          w            NLMS                    ⁡                      (                          ⅈ              +              1                        )                          =                                            w              NLMS                        ⁡                          (              ⅈ              )                                -                                    Δ              ~                        ⁢                                                                                y                    ⁡                                          (                      ⅈ                      )                                                        ⁢                                                            ⅇ                      *                                        ⁡                                          (                      ⅈ                      )                                                                                                                                                      y                      ⁡                                              (                        ⅈ                        )                                                                                                  2                                            .                                                          (        3        )            As shown, new NLMS coefficient wNLMS(i+1) uses a step size {tilde over (Δ)}, which reduces the complexity of tuning the step size.
Error Calculation
The accuracy of NLMS equalizer 104 in approximating the original pre-transmission signal is measured by error signal e(i). Thus, a smaller error e(i) represents improved equalizer performance. Error signal e(i) is obtained by comparing equalized output {circumflex over (x)}(i) of FIR filter 110 to a reference signal x(i) as shown in Equation (4) below:e(i)={circumflex over (x)}(i)−x(i)  (4)Reference signal x(i) represents an expected value for the received signal, neglecting the effects of transmission. Thus, error signal e(i) decreases as equalized output {circumflex over (x)}(i) more closely approximates expected reference x(i) known by receiver 100.
In typical transmissions, a large portion of the transmitted signal is not known by the receiver. However, a pilot signal z(i), which contains a known sequence of bits, may be transmitted for training and tracking purposes. Substituting pilot z(i) for reference x(i) in Equation (4) yields error signal e′(i) as shown in Equation (5):e′(i)=z(i)−{circumflex over (x)}(i)  (5)The complex conjugate of error signal e′(i) may then be substituted for error e*(i) in Equation (3) to produce new NLMS coefficient wNLMS(i+1).
In a 3rd Generation Partnership Project (3GPP) application, receivers are equalized using the common pilot channel (CPICH). Furthermore, CPICH has a scrambled sequence Cscram(i) and a spread sequence Cch(i) which are known by the receiver. For 3GPP Release 5 compatible receivers, either the primary pilot channel (PCPICH), the secondary pilot channel (SCPICH), or both may be used for continuous tracking and training. SCPICH has a spreading sequence and a scrambling code which are unique from PCPICH.
Pilot signal power in 3GGP and other applications is typically limited to 10 percent of the total transmission power. Since the pilot signal represents only a small portion of the total received signal power, signal error e′(i) never closely approximates zero. Additionally, since only pilot z(i) is used in calculating the gradient estimate, the unknown data symbols of input signal y(i) contribute to the gradient noise. In order to minimize error e′(i), and thus increase the performance of equalization, the pilot signal power can be increased. Increasing pilot signal power, however, reduces the amount of data that can be transmitted along with the pilot signal.